After doing research on the possibility of making invisible buttons under a wooden worktop, I came across an invention by Loxone (company specializing in home automation). The "Touch Surface" is an object that has just been pasted under a work surface (up to 30mm thick) allowing to detect a press on a specific area of the work surface. I would like to do a similar project with my arduino but I can't find a capacitive sensor allowing detection at such a distance (AT42QT1011, MTCH101...). Do you have an idea or a component reference to offer me?
Possible - sure. Difficult - you bet. My record is close to half a meter, using Theremin type detection. Ridiculously sensitive (best keep doors closed - that kind of sensitive), it's based on LC oscillators. That AN is talking about 0.5-5 pF changes; the theremin circuits sense changes in the fF (femto Farad) order of magnitude. The main problem with that technique may be directionality - specifically the lack of it.
Go get some TTP223 Touch Sensors and experiment with placing your touch pads under the wooden surface. You will want to use fairly large pads - a few square inches each.
The rcwl-0516 is one such sensor that can be used with the Arduino, works great for motion detection in its general environment.
It's not radar, nor doppler, or whatever those advertisements say. It's actually working at about 6 GHz (so at least it is in the microwave part of the spectrum) and it looks for changes in interference patterns. The large range and full surround sensitivity makes these sensors useless as touch/proximity sensor as the OP is looking for.